Question

joshua conducted an independent samples t-test and found t(20) = 10.25, p < .05. He then calculated his effect size and obtained a value of d = 0.05. What should Joshua say in the reports on his results?

Answer 1

Answer:

On this case since the p value is less than 0.05 then the results are significant. So then Joshua can say that the t-test conducted is significant. And on this case makes sense report the effect size.

Step-by-step explanation:

Effect size is defined as a "quantitative measure of the magnitude of the experimenter effect". If we have a high value for the effect size then we can conclude that we have a stronger relationship between two variables.

t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

The independent t-test, is an statistical test in order to determine if we have statistically significant difference between the means of two unrelated groups.

We can check for example the following hypothesis:

Null hypothesis:$\mu_{1} \leq \mu_{2}$

Alternative hypothesis:$\mu_{1} > \mu_{2}$

The statistic for this test is given by:

$t=\frac{\bar X_{1}-\bar X_{2}}{\sqrt{\frac{s^2_{1}}{n_{1}}+\frac{s^2_{2}}{n_{2}}}}$ (1)

The value obtained after apply the formula (1) was 10.25.

And the degreed of freedom are calculated from:

$df=n_1 +n_2 -2 =20$

On this case since the p value is less than 0.05 then the results are significant. So then Joshua can say that the t-test conducted is significant. And on this case makes sense report the effect size.

Usually when the Cohen effect size value d=0.2 or lower we can consider this as a 'small' effect size, and that's our case.